Form measuring device and method of aligning form data

ABSTRACT

A form measuring device includes: a measuring unit configured to detect a height at each position in a reference axis direction of a measured object and measure a cross-sectional form of the measured object; and an arithmetic unit configured to synthesize a plurality of form measurement data, obtained by repeated measurements of the form of the same measured object by the measuring unit, and calculate synthesized form measurement data. In the synthesis of the form measurement data, the arithmetic unit is configured to calculate shift amounts in the reference axis direction and a height direction of the form measurement data with respect to the synthesized form measurement data and align the form measurement data in the reference axis direction and the height direction based on the calculated shift amount.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2009-243760, filed on Oct. 22,2009, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of aligning form data (profiledata), which is obtained by a form measuring instrument, an imagemeasuring instrument, a three-dimensional measuring instrument, and thelike, and a form measuring device using the method.

2. Description of the Related Art

Conventionally, there have been known various form measuring deviceswhich measure a three-dimensional form of an object to be measured(hereinafter, “measured object”) in a noncontact manner using an opticalsystem. Known examples of a form measuring device, which enablesthree-dimensional measurement of a measured object having a minuteunevenness such as a micromachine and an LSI, include a white lightinterferometer. The white light interferometer applies white light froma white light source to a measured object and a reference surface tointerfere white lights reflected from the measured object and thereference surface. The white light interferometer moves the referencesurface in an optical axis direction to detect a reference surfaceposition having the highest interfering light intensity, thereby tomeasure the height in the optical axis direction of the measured objectbased on the reference surface position (International Publication WO2006/068217).

However, in the above conventional form measuring device, if a measuredobject having unevenness is measured as in line-width measurement of anIC package, there is a problem that data in the uneven portion is likelyto have defect. If data has defect, stable and highly accuratemeasurement results cannot be obtained.

In view of the above problems, an object of the invention is to providea form measuring device, which suppresses the influence of data defectin an uneven portion and can obtain stable and highly accuratemeasurement results, and a method of aligning form data.

SUMMARY OF THE INVENTION

A form measuring device according to the invention includes: a measuringunit configured to detect a height at each position in a reference axisdirection of a measured object and measure a cross-sectional form of themeasured object; and an arithmetic unit configured to synthesize aplurality of form measurement data obtained by repeated measurements ofthe form of the same measured object by the measuring unit, andcalculate synthesized form measurement data, in the synthesis of theform measurement data, the arithmetic unit being configured to calculateshift amounts in the reference axis direction and a height direction ofthe form measurement data with respect to the synthesized formmeasurement data and align the form measurement data in the referenceaxis direction and the height direction based on the calculated shiftamounts.

A form measuring device according to the invention includes anarithmetic unit, between form measurement data I_(L) comprising data ofa height at each position in a reference axis direction of a measuredobject and synthesized form measurement data I_(R) obtained bysynthesizing the form measurement data I_(L), when a shift amount of apixel (integer number) in the reference axis direction is represented asd, a shift amount of a sub-pixel (real number) in the reference axisdirection is represented as Δd, and a shift amount in a height directionis represented as Δz, the arithmetic unit being configured to repeatedlyperform such a calculation that two-dimensional linear simultaneousequations based on

$\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{Min} \right.$

are solved to obtain Δd and Δz until a predetermined convergencecondition is satisfied to thereby calculate the shift amounts in thereference axis direction and the height direction, the arithmetic unitbeing configured to shift the form measurement data by the calculatedshift amounts in the reference axis direction and the height directionand align the form measurement data with the synthesized formmeasurement data.

A method of aligning form data according to the invention comprises by acomputer: between form measurement data I_(L) comprising data of aheight at each position in a reference axis direction of a measuredobject and synthesized form measurement data I_(R) obtained bysynthesizing the form measurement data I_(L), when a shift amount of apixel (integer number) in the reference axis direction is represented asd, a shift amount of a sub-pixel (real number) in the reference axisdirection is represented as Δd, and a shift amount in a height directionis represented as Δz, repeatedly performing such a calculation thattwo-dimensional linear simultaneous equations based on

$\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{Min} \right.$

are solved to obtain Δd and Δz until a predetermined convergencecondition is satisfied to thereby calculate the shift amounts in thereference axis direction and the height direction; and shifting the formmeasurement data by the calculated shift amounts in the reference axisdirection and the height direction and aligning the form measurementdata with the synthesized form measurement data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a constitution of a form measuringdevice according to a first embodiment of the invention;

FIG. 2 is a flowchart showing an operation of an arithmetic processingunit in the form measuring device;

FIG. 3 is a view for explaining a method of measuring a cross-sectionalform in the form measuring device;

FIG. 4 is a view for explaining the method of measuring across-sectional form;

FIG. 5 is a flowchart for explaining an alignment processing in thesynthesis of measurement data of a cross-sectional form in the formmeasuring device; and

FIGS. 6A and 6B are views showing results of the alignment processing.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Next, a form measuring device and a form measuring method according anembodiment of the invention will be described in detail.

FIG. 1 is a view showing a constitution of a white light interferometerwhich is the form measuring device according to the present embodiment.In the present embodiment, although the white light interferometer is aMichelson interferometer, other equal optical path interferometers suchas a Mirau interferometer may be used. The interferometer may be usedwith another optical measuring device such as an image measuring device.

A light source 1 is a white light source having a broadband spectrum,such as a halogen lamp, a xenon lamp, a mercury lamp, a metal-halidelamp, and an LED. White light emitted from the light source 1 iscollimated by a collimator lens 2 to be divided into two directions by abeam splitter 3. One of the divided lights is applied to a measurementsurface of a workpiece 4 which is an object to be measured, and theother is applied to a reference surface of a reference plate 5. Thewhite light reflected from the measurement surface and the white lightreflected from the reference surface are synthesized by the beamsplitter 3, and interfering light at this time is imaged by a CCD camera8 through an imaging lens 7.

The reference plate 5 is moved and scanned in the optical axis directionby a drive unit 6 such as a piezoelectric element, and an interferenceimage at each scanning position is sampled by the CCD camera 8 to bestored in an image memory 9. An arithmetic processing unit 10 obtainsform measurement data (hereinafter referred to as “surface data”) of themeasurement surface of the workpiece 4 based on the intensity of theinterfering light at each position of the measurement surface of theworkpiece 4, and the scanning position of the reference plate 5 inputfrom an encoder 14. Then, the arithmetic processing unit 10 extractscross-section data (hereinafter referred to as “profile data”) from thesurface data. An input unit 11 inputs data required for measurement tothe arithmetic processing unit 10. An output unit 12 outputs measurementresults obtained by the arithmetic processing unit 10. A display unit 13displays information required for input operation and measurementresults.

Next, a profile measurement method by the white light interferometerwill be described.

FIG. 2 is a flowchart showing a measurement processing in the arithmeticprocessing unit 10. The processing in the arithmetic processing unit 10includes: a process of measuring the surface data in a region to beevaluated of the measurement surface of the workpiece 4 (S1); a processof extracting profile data from the measured surface data (S2); aprocess of aligning the profile data obtained in the current measurementwith the profile data obtained in previous measurements (S3); and aprocess of synthesizing the aligned current profile data with theprofile data obtained in previous measurements (S4), and these processesS1 to S4 are repeated predetermined times. Hereinafter, each processwill be described in detail.

(1) Surface data measurement processing of region to be evaluated (S1)and extraction processing of profile data (S2)

The white light from the light source 1 is reflected on the measurementsurface of the workpiece 4 and the reference surface of the referenceplate 5 to be synthesized by the beam splitter 3. The interferingintensity at that time is changed by moving or scanning the referenceplate 5 in the optical axis direction by the piezoelectric element 6. Byvirtue of the use of low coherent white light, a range where aninterference pattern is generated can be narrowed. According to thisconstitution, for example, as shown in FIG. 3, a change of interferinglight intensity at each position of the measurement surface caused bythe movement or scanning of the reference surface occurs at a phasecorresponding to the height of the measurement surface (a Z directionposition). Therefore, the scanning position on the reference surface,where the peak value of the change in the interfering light intensity ateach position of the measurement surface is observed, can be obtained asthe height of the corresponding portion of the measurement surface.

FIG. 4 is a view for explaining an example of a processing of obtainingthe peak position of the change in the interfering light intensity fromthe change in the interfering light intensity at each position. In thisprocessing, a predetermined geometric element (for example, a straightline or a curve) A is fitted to an interfering light intensity columnobtained by moving and scanning the reference surface. Alternatively,the obtained interfering light intensity column is smoothed to obtainthe geometric element (for example, a straight line or a curve) A. Next,the obtained geometric elements A are shifted in plus and minusdirections of a intensity axis, and threshold levels B and C are set.The interfering light intensity exceeding the threshold levels isobtained as a peak position candidate point. Then, a barycenter of aregion where the peak position candidate points are most densely locatedis obtained as a peak position P. By virtue of this processing, the peakposition P can be obtained at high speed, reducing the number ofprocessing points. The peak position P obtained as described abovecorresponds to the height (Z value) at the measurement point. Byobtaining the Z value at each position on the measurement surface, thesurface data of the workpiece 4 can be obtained. The profile data on acertain cross section can be obtained by extracting data in an arbitrarydirection from the surface data (S2).

(2) Alignment of Profile Data (S3)

When the uneven workpiece 4 is measured by the white lightinterferometer as in line-width measurement of an IC chip, the data inthe uneven portion is likely to have defect. Thus, there occur suchproblems that the number of data sufficient for the line-widthmeasurement cannot be obtained, and stable line-width values cannot beobtained in repeated measurements.

Thus, in the present embodiment, when a certain region is a region to beevaluated, a plurality of cross-sectional data required for theline-width measurement are obtained to be synthesized, whereby thenumber of the defect portions of unevenness is reduced, so that stableline-width values can be obtained even in repeated measurements (S4).

However, the workpiece 4 is not always placed horizontally, andtherefore, before synthesis of the cross sections, it is essential toalign some taken cross sections. In this case, the more the number ofthe cross sections to be processed, the better, because the number ofdefect portions is reduced. Thus, depending on a workpiece, the numberof the cross sections may be considerably increased, and thus someingenuity is required for the alignment processing. For this type ofalignment method, a best-fitting processing using a shortest distancehas been known. However, in the best-fitting processing, since thecalculation amount is large, it is slightly difficult to realize areal-time processing in a production line. Thus, a stereo matchingmethod is expanded, and a high-speed alignment processing betweenprofile data is realized.

Hereinafter, the alignment processing will be described.

[Basic Principle]

Generally, in the stereo matching method between two images, one data isrepresented as I_(L), and the other data is represented as I_(R). WhenI_(L) is moved to be fitted to I_(R), d is defined as a shift amount ofa pixel (integer number), and Δd as a shift amount of a sub-pixel (realnumber). In this case, the approximation can be realized as follows,using a Taylor expansion:

$\begin{matrix}{{I_{L}\left( {x + d + {\Delta \; d}} \right)} \approx {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; {d.}}}} & (1)\end{matrix}$

If an evaluation amount φ is defined as

φ=ρ{I _(L)(x+d+Δd)−I _(R)(x)}²  (2),

the following formula (3) is obtained from the formula (1):

$\begin{matrix}{{{\sum\left\{ {{I_{L}\left( {x + d + {\Delta \; d}} \right)} - {I_{R}(x)}} \right\}^{2}} \approx {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)}} \right\}^{2}}};} & (3)\end{matrix}$

therefore, Δd satisfying the following formula (4) only needs to beobtained:

$\begin{matrix}\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)}} \right\}^{2}}\rightarrow{{Min}.} \right. & (4)\end{matrix}$

In the above method, although the alignment in an X direction can beperformed, the alignment in a Z direction cannot be performed. Thus, inthe above formula, the value I_(L) in the Z direction is represented asI_(L)+ΔZ, and it is considered that the alignment in the Z direction isperformed at the same time. In this case, Δd and ΔZ satisfying theflowing formula (5) only need to be obtained:

$\begin{matrix}\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{{Min}.} \right. & (5)\end{matrix}$

Since the formula (5) is reduced to the problem of solving simpletwo-dimensional linear simultaneous equations, the computation load isvery low. In the application to an actual problem, the formula (5) isrepeatedly solved, and the final solution may be obtained while updatingan amount of movement.

[Practical Algorithm Considering Discretization (Sampling) in XDirection]

In normal measurement, Z value data is sampled in the X direction with aconstant sampling interval, and therefore when the formula (5) issolved, if the calculation is performed considering the integer part ofthe result of the division of the movement amount in the X directionwith a constant sampling interval and the real part of the remainder,the solution can be obtained with high accuracy.

FIG. 5 is a flowchart showing a processing of obtaining the actualmovement amounts in the X and Z directions.

First, “1” as an initial value is substituted into a repetitionfrequency m (S11).

Here, the movement amounts in the X and Z directions after therepetition of m times are expressed respectively as u^((m)) and v^((m)),and their initial values are set (S12). The initial value may be set sothat the barycentric positions of two profile data coincide with eachother, for example, or may be set so that specified data points (forexample, the peak values of the profile data) coincide with each other.With regard to two data which do not deviate so much, the initial valuemay be 0.

Next, amounts of correction Δu^((m+1)) and Δv^((m+1)) of the movementamounts in each axial direction in each calculation cycle of therepeated calculations of the movement amount u^((m)) in the X directionand the movement amount v^((m)) in the Z direction are calculated asfollows (S13).

The integer part of the result of the division of the movement amountu^((m)) in the X direction with a sampling interval is u^((m)) _(d), andthe real part of the remainder is u^((m)) _(Δd). More commonly, whenconsidering the weight of a data point on the I_(L) side as w_(L), andconsidering the weight of a data point on the I_(R) side as w_(R), theformula (5) is the following formula (6):

$\begin{matrix}\left. {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\left( {u_{\Delta \; d}^{(m)} + {\Delta \; u^{({m + 1})}}} \right)} - {I_{R}(x)} + v^{(m)} + {\Delta \; v^{({m + 1})}}} \right\}^{2}}}\rightarrow{{Min}.} \right. & (6)\end{matrix}$

Thus, the correction amounts Δu^((m+1)) and Δv^((m+1)) can be obtainedby solving the following formula (7):

$\begin{matrix}{{\begin{pmatrix}\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\left\{ \frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x} \right\}^{2}\end{matrix} & \begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} & {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}\end{pmatrix}\begin{pmatrix}{\Delta \; u^{({m + 1})}} \\{\Delta \; v^{({m + 1})}}\end{pmatrix}} = {\begin{pmatrix}\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\}\end{matrix}\end{pmatrix}.}} & (7)\end{matrix}$

In the application to the measurement data, calculation may be performedby replacing a differential with a difference. When the correctionamounts Δu^((m+1)) and Δv^((m+1)) are obtained, the movement amount ineach axial direction is updated by the following formula (8) (S15):

u ^((m+1)) =u ^((m)) +Δu ^((m+1))

v ^((m+1)) =v ^((m)) +Δv ^((m+1))  (8).

It is determined that m←m+1 (S16), and updating is sequentiallyperformed until Δu^((m+1)) and Δv^((m+1)) become satisfactorily small,whereby the final solution is reached (S14, S17).

(3) Synthesis of Profile Data (S4)

In a processing of synthesizing profile data (S4), newly obtainedprofile data is shifted in the X and Z directions by the movementamounts u^((m)) and v^((m)) in the X and Z directions obtained by theabove processing and then synthesized with previously synthesizedprofile data.

FIG. 6A shows a state in which newly obtained profile data E is shiftedin the X and Z directions with respect to original profile data D. FIG.6B shows a state in which the profile data E is shifted in the X and Zdirections as shown by E′ by the above method to be superposed on theoriginal profile data D.

As shown in FIGS. 6A and 6B, by virtue of the above stereo matchingprocessing, the profile data can be superposed at high speed and withhigh accuracy; therefore, the influence of data defect in an unevenportion is suppressed, and stable and highly accurate measurementresults can be obtained.

The above point will be described in more detail. As the matching of theprofile data, there has been known a best-fitting processing forobtaining a shortest distance and the like. However, in the best-fittingprocessing, substantially the same objects are to be compared andaligned, such as between a design value and measurement data in anappropriate portion and between measurement data obtained by measuringthe same position. Therefore, a complex and advanced processing such asshortest distance calculation with a design value and making datacorresponding to each other is required.

Meanwhile, the data alignment between profile data utilizing stereomatching is basically applied to some image measurement data with thesame measured object and is applied only to the X direction of a pixel(see, “Stereo Matching by Adaptive Window Based on StatisticalModel—Analysis and Experiments Using One-dimensional Signal,” by Okutomiand Kanade, The Institute of Electronics, Information and CommunicationEngineers Paper D-11, Vol. J74-D-11, No. 6, pp 669-677, 1991). Thus, thedata alignment is used only for the limited purpose.

In the present embodiment, theoretical extension is attempted so thatnot only the image measurement data but also two profile data measuredat the same pitch are aligned with each other in the both X and Zdirections, whereby a simple and high-speed processing can be realized.

In the above embodiment, although the invention is applied to the whitelight interferometer, the invention may be obviously applied to otherform measuring devices such as an image measuring device and a laserdisplacement gauge.

1. A form measuring device comprising: a measuring unit configured todetect a height at each position in a reference axis direction of ameasured object and measure a cross-sectional form of the measuredobject; and an arithmetic unit configured to synthesize a plurality ofform measurement data obtained by repeated measurements of the form ofthe same measured object by the measuring unit, and calculatesynthesized form measurement data, in the synthesis of the formmeasurement data, the arithmetic unit being configured to calculateshift amounts in the reference axis direction and a height direction ofthe form measurement data with respect to the synthesized formmeasurement data and align the form measurement data in the referenceaxis direction and the height direction based on the calculated shiftamounts.
 2. The form measuring device according to claim 1, whereinbetween form measurement data I_(L) and synthesized form measurementdata I_(R) obtained by synthesizing the form measurement data I_(L),when a shift amount of a pixel (integer number) in the reference axisdirection (x direction) is represented as d, a shift amount of asub-pixel (real number) in the reference axis direction is representedas Δd, and a shift amount in the height direction is represented as Δz,the arithmetic unit is configured to repeatedly perform such acalculation that two-dimensional linear simultaneous equations based on$\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{Min} \right.$are solved to obtain Δd and Δz until a predetermined convergencecondition is satisfied to thereby calculate the shift amounts in thereference axis direction and the height direction.
 3. The form measuringdevice according to claim 2, wherein when a movement amount in thereference axis direction and a movement amount in the height directionafter the repetition of m times are represented respectively as u^((m))and v^((m)), amounts of correction of the movement amounts in each axialdirection in each calculation cycle of the repeated calculations ofu^((m)) and v^((m)) are represented respectively as Δu^((m+1)) andΔv^((m+1)), an integer part of a result of division of u^((m)) with asampling interval is represented as u^((m)) _(d), and a real part of aremainder is represented as u^((m)) _(Δd), and a weight of a data pointon the I_(L) side is represented as w_(L), and a weight of a data pointon the I_(R) side is represented as w_(R), the arithmetic unit isconfigured to solve ${\begin{pmatrix}\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\left\{ \frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x} \right\}^{2}\end{matrix} & \begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} & {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}\end{pmatrix}\begin{pmatrix}{\Delta \; u^{({m + 1})}} \\{\Delta \; v^{({m + 1})}}\end{pmatrix}} = \begin{pmatrix}\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\}\end{matrix}\end{pmatrix}$ to thereby obtain the correction amounts Δu^((m+1)) andΔv^((m+1)), correct the movement amounts u^((m)) and v^((m)) until thecorrection amounts Δu^((m+1)) and Δv^((m+1)) are smaller than apredetermined value, and repeat the calculation processing.
 4. The formmeasuring device according to claim 1, wherein the measuring unitcomprises: a light source having a broadband spectrum; an optical systemconfigured to guide light from the light source to the measured objectand a reference surface, synthesize lights reflected from the measuredobject and the reference surface, and to thereby generate an interferinglight intensity distribution image showing an interfering lightintensity changed by an optical path length difference between a firstoptical path length from the light source to the measured object and asecond optical path length from the light source to the referencesurface, the interfering light intensity corresponding to eachmeasurement position in a measurement surface of the measured object; animaging unit configured to image the interfering light intensitydistribution image output from the optical system; an optical pathlength changing unit configured to change a difference of the opticalpath length between the first optical path length and the second opticalpath length; and an image storage unit configured to sequentially storethe interfering light intensity distribution images changed with achange in the difference of the optical path length imaged by theimaging unit, wherein the arithmetic unit is configured to obtain a peakvalue of a change in the interfering light intensity from an interferinglight intensity column showing the change in the interfering lightintensity with the change in the optical path length difference at eachmeasurement position of the interfering light intensity distributionimage stored in the image storage unit, obtain, as a height of themeasured object, a position in the optical axis direction at eachmeasurement position of the measured object where the peak value isobtained, and obtain a height at each position in a predeterminedreference axis direction perpendicular to the optical axis direction. 5.The form measuring device according to claim 4, wherein the arithmeticunit is configured to obtain, as a candidate point of a peak position, aposition of the interfering light intensity column where the interferinglight intensity exceeding a predetermined threshold value is obtained,and obtain the height based on a barycenter of a region where thecandidate points of the peak position are most densely located.
 6. Theform measuring device according to claim 5, wherein the arithmetic unitis configured to fit a predetermined geometric element to theinterfering light intensity column and shift the geometric element in aplus or minus direction of an intensity axis direction to thereby setthe threshold value.
 7. The form measuring device according to claim 6,wherein the arithmetic unit is configured to smooth the interferinglight intensity to thereby calculate the geometric element.
 8. A formmeasuring device comprising an arithmetic unit, between form measurementdata I_(L) comprising data of a height at each position in a referenceaxis direction of a measured object and synthesized form measurementdata I_(R) obtained by synthesizing the form measurement data I_(L),when a shift amount of a pixel (integer number) in the reference axisdirection is represented as d, a shift amount of a sub-pixel (realnumber) in the reference axis direction is represented as Δd, and ashift amount in a height direction is represented as Δz, the arithmeticunit being configured to repeatedly perform such a calculation thattwo-dimensional linear simultaneous equations based on$\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{Min} \right.$are solved to obtain Δd and Δz until a predetermined convergencecondition is satisfied to thereby calculate the shift amounts in thereference axis direction and the height direction, the arithmetic unitbeing configured to shift the form measurement data by the calculatedshift amounts in the reference axis direction and the height directionand align the form measurement data with the synthesized formmeasurement data.
 9. The form measuring device according to claim 8,wherein when a movement amount in the reference axis direction and amovement amount in the height direction after the repetition of m timesare represented respectively as u^((m)) and v^((m)), amounts ofcorrection of the movement amounts in each axial direction in eachcalculation cycle of the repeated calculations of u^((m)) and v^((m))are represented respectively as Δu^((m+1)) and Δv^((m+1)), an integerpart of a result of division of u^((m)) with a sampling interval isrepresented as u^((m)) _(d), and a real part of a remainder isrepresented as u^((m)) _(Δd), and a weight of a data point on the I_(L)side is represented as w_(L), and a weight of a data point on the I_(R)side is w_(R), the arithmetic unit is configured to solve${\begin{pmatrix}\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\left\{ \frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x} \right\}^{2}\end{matrix} & \begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} & {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}\end{pmatrix}\begin{pmatrix}{\Delta \; u^{({m + 1})}} \\{\Delta \; v^{({m + 1})}}\end{pmatrix}} = \begin{pmatrix}\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\}\end{matrix}\end{pmatrix}$ to thereby obtain the correction amounts Δu^((m+1)) andΔv^((m+1)), correct the movement amounts u^((m)) and v^((m)) until thecorrection amounts Δu^((m+1)) and Δv^((m+1)) are smaller than apredetermined value, and repeat the calculation processing.
 10. A methodof aligning form data comprising by a computer: between form measurementdata I_(L) comprising data of a height at each position in a referenceaxis direction of a measured object and synthesized form measurementdata I_(R) obtained by synthesizing the form measurement data I_(L),when a shift amount of a pixel (integer number) in the reference axisdirection is represented as d, a shift amount of a sub-pixel (realnumber) in the reference axis direction is represented as Δd, and ashift amount in a height direction is represented as Δz, repeatedlyperforming such a calculation that two-dimensional linear simultaneousequations based on are$\left. {\sum\; \left\{ {{I_{L}\left( {x + d} \right)} + {\frac{{I_{L}\left( {x + d} \right)}}{x}\Delta \; d} - {I_{R}(x)} + {\Delta \; z}} \right\}^{2}}\rightarrow{Min} \right.$solved to obtain Δd and Δz until a predetermined convergence conditionis satisfied to thereby calculate the shift amounts in the referenceaxis direction and the height direction; and shifting the formmeasurement data by the calculated shift amounts in the reference axisdirection and the height direction and aligning the form measurementdata with the synthesized form measurement data.
 11. The method ofaligning form data according to claim 10, wherein when a movement amountin the reference axis direction and a movement amount in the heightdirection after the repetition of m times are represented respectivelyas u^((m)) and v^((m)), amounts of correction of the movement amounts ineach axial direction in each calculation cycle of the repeatedcalculations of u^((m)) and v^((m)) are represented respectively asΔu^((m+1)) and Δv^((m+1)), an integer part of a result of division ofu^((m)) with a sampling interval is represented as u^((m)) _(d), and areal part of a remainder is represented as u^((m)) _(Δd), and a weightof a data point on the I_(L) side is represented as w_(L), and a weightof a data point on the I_(R) side is represented as w_(R),${\begin{pmatrix}\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\left\{ \frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x} \right\}^{2}\end{matrix} & \begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} & {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}\end{pmatrix}\begin{pmatrix}{\Delta \; u^{({m + 1})}} \\{\Delta \; v^{({m + 1})}}\end{pmatrix}} = \begin{pmatrix}\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\} \\\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}\end{matrix} \\\begin{matrix}{- {\sum{{w_{L}\left( {x + u_{d}^{(m)}} \right)}{w_{R}(x)}}}} \\\left\{ {{I_{L}\left( {x + u_{d}^{(m)}} \right)} - {I_{R}(x)} + {\frac{{I_{L}\left( {x + u_{d}^{(m)}} \right)}}{x}u_{\Delta \; d}^{(m)}} + v^{(m)}} \right\}\end{matrix}\end{pmatrix}$ is solved by a computer, whereby the correction amountsΔu^((m+1)) and Δv^((m+1)) are obtained, the movement amounts u^((m)) andv^((m)) are corrected until the correction amounts Δu^((m+1)) andΔv^((m+1)) are smaller than a predetermined value, and the calculationprocessing is repeated.